 An hp-mixed discontinuous Galerkin method for the biharmonic eigenvalue problemJinhua Feng, Shixi Wang, Hai Bi and Yidu Yang Applied Mathematics and Computation, 2023, vol. 450, issue C Abstract: The biharmonic equation/eigenvalue problem is one of the fundamental model problems in mathematics and physics, and has wide applications. In this paper, we study an hp-mixed discontinuous Galerkin method for the biharmonic eigenvalue problem. Based on the work of Gudi et al. [J Sci Comput, 37 (2008)], using piecewise polynomials of degree p≥3, we derive the a priori error estimates of the approximate eigenfunction in the broken H1 norm and L2 norm which are optimal in h and suboptimal in p. When p=2, the approximate eigenfunctions converge but with only suboptimal convergence rate. When p≥2 and the eigenfunction u∈Hs(Ω)(s≥p+1), we prove that the convergence rate of approximate eigenvalues reaches 2p−2 in h and p−(2s−7) in p. We also discuss the a posterior error estimates of the approximate eigenvalues and implement the adaptive calculation. Numerical experiments show that the methods are easy to implement and can efficiently compute biharmonic eigenvalues. Keywords: The biharmonic eigenvalue; Mixed DG method; hp approximations; A priori error analysis; A posterior error analysis (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:450:y:2023:i:c:s0096300323001388 DOI: 10.1016/j.amc.2023.127969 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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